The diagram shows two mathematically similar shapes with areas 295c * m ^ 2 and 159.5c * m ^ 2
The width of the larger shape is 17 cm.
Calculate the width of the smaller shape.
Let's denote the width of the smaller shape as x.
We are given that the area of the larger shape is 295c * m^2 and its width is 17 cm.
So, the length of the larger shape is 295c * m^2 / 17 cm.
Since the shapes are mathematically similar, their corresponding sides are proportional. Thus, we can write the following equation:
(x cm) / (295c * m^2 / 17 cm) = sqrt((159.5c * m^2) / (295c * m^2))
Simplifying this equation, we get:
(x cm) / (295c * m^2 / 17 cm) = sqrt(159.5c / 295c)
(x cm) / (295c * m^2 / 17 cm) = sqrt(159.5 / 295)
Now, cross-multiplying and simplifying the equation, we get:
(x cm) * 17 cm = sqrt(159.5 / 295) * (295c * m^2)
17x cm^2 = sqrt(159.5 / 295) * 295c * m^2
Now, dividing both sides of the equation by 17, we find:
x cm = (sqrt(159.5 / 295) * 295c * m^2) / 17
Hence, the width of the smaller shape is (sqrt(159.5 / 295) * 295c * m^2) / 17 cm.